The Shannon Decomposition Function is a Boolean function of three variables which uses a control variable, C, to select between two other inputs variables, X and Y, so as to provide the logic function (C and X) or (C and Y). This function is particularly useful in digital arithmetic because an arbitrarily complex Boolean function of N variables can be decomposed using the Shannon function into a sequence of simpler functions each of not more than three variables. Thus, a set of electronic circuits that implements the Shannon Decomposition Function can be interconnected together to implement an arbitrary combinatorial Boolean function of N Variables in the form of an electronic circuit. Since a complex logic function can be assembled solely using a regular cellular array of Shannon Decomposition Functions, the circuit that implements the Shannon Decomposition Function can be referred to appropriately as a Shannon Cell, and a suitably large regular array of Shannon Cells can implement an arbitrarily complex Boolean combinatorial function of N variables.
A Shannon Cell and arrays of Shannon Cells can be implemented using conventional electronic components such a bipolar and field effect transistors. However, the practical and physical limits upon the ability to downscale these components places a minimum constraint upon the integrated circuit area used to implement this circuitry. This is a significant drawback in light of the everpressing need to increase the functional density of integrated electronic systems.
Furthermore, with the advent of nanoelectronics, or quantum effect electronics, device geometries can be downscaled to achieve significant increases in the functional densities of integrated electronic systems. Although advances have been made in the development of quantum effect devices, the few devices which may have applications in digital circuits have significant limitations. For example, devices such as those disclosed by Chou, Allee, Pease, and Harris in "Lateral Resonant Tunneling Transistors Employing Field-Induced Quantum Wells and Barriers," Proceedings of the IEEE, Volume 79, No. 8, August 1991, pp. 1131-39, display certain characteristics of semiconductor switching devices. Through the use of an electric field, quantized regions can be created between depletion-region potential barriers, and resonant tunneling can be observed. Thus, electric current can be switched "ON" or "OFF", depending on the strength of the electric fields. The performance of such devices, however, is highly dependent upon precise dopant concentrations, and they must be operated only at low temperatures.
Therefore, a need has arisen for an implementation of the Shannon decomposition function in the form of an electronic circuit using nanoelectronic, or quantum effect, devices.